Constructive Asymptotic Bounds of Locally Repairable Codes via Function Fields

Locally repairable codes have been investigated extensively in recent years due to practical applications in distributed and cloud storage systems. However, there are few asymptotic constructions of locally repairable codes in the literature. In this paper, we provide a new explicit asymptotic const...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on information theory Vol. 66; no. 9; pp. 5395 - 5403
Main Authors Ma, Liming, Xing, Chaoping
Format Journal Article
LanguageEnglish
Published New York IEEE 01.09.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Alphabets
asymptotic bounds
Asymptotic properties
Cloud computing
Encoding
Fields (mathematics)
Frequency modulation
Geometry
Indexes
local expansions
Locally repairable codes
Poles and towers
Riemann-Roch spaces
Storage systems
Upper bound
Online AccessGet full text

Cover

More Information
Summary:Locally repairable codes have been investigated extensively in recent years due to practical applications in distributed and cloud storage systems. However, there are few asymptotic constructions of locally repairable codes in the literature. In this paper, we provide a new explicit asymptotic construction of locally repairable codes over arbitrary finite fields from local expansions of functions at a rational place. This construction gives a Tsfasman-Vladut-Zink type bound for locally repairable codes. Its main advantage is that there are no constraints on both locality and alphabet size. Furthermore, we show that the Gilbert-Varshamov type bound of locally repairable codes over non-prime finite fields can be improved for sufficiently large alphabet sizes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2020.2970419